No service, means that it can not talk to any of the towers.
This could be a number of things.
A ) assuming you are in an area with coverage? B ) your account is ok? Its paid up, not canceled? If its pay as you go, there is money in there?
C ) Assuming all that is ok...you are down to PHONE or SIM CARD problem. If the sim card is acting flakey, then it may not connect properly. If you can go to a local rogers store, they should be able to help exchange your sim card for you.
Welcome to the Community. I am sorry to hear you are having signal issues .
This can be caused by either;
Not in our coverage area
Device or SIM card issue
Or as @Gdkitty pointed out, possibly an inactive account.
Have you tried switching the SIM card into another device to see if the problem persists? This is a good way to narrow down whether it is a device or SIM card issue.
Is this happening in a certain location? Try to see if you can access service in another location (main level of house or building) or area.
If you have tried these steps with no success I would advise you to visit your nearest Rogers corporate store or (if you have access to another phone) contact customer service 1 -888-764-3771 to have them look into your account.